Frontiers of Mathematics in China

, Volume 3, Issue 3, pp 371–397

Construct irreducible representations of quantum groups Uq(ƒm(K))

Research Article

DOI: 10.1007/s11464-008-0027-8

Cite this article as:
Tang, X. Front. Math. China (2008) 3: 371. doi:10.1007/s11464-008-0027-8


In this paper, we construct families of irreducible representations for a class of quantum groups Uq(ƒm(K)). First, we give a natural construction of irreducible weight representations for Uq(ƒm(K)) using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of Uq(ƒm(K)). As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.


Hyperbolic algebraspectral theoryWhittaker modulesquantum group



Copyright information

© Higher Education Press and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of Mathematics & Computer ScienceFayetteville State UniversityFayettevilleUSA